Methodologies for broadband reverberation data processing and analysis

Indian Journal of Geo-Marine Sciences Vol. 44(2), February 2015, pp. 245-251 Methodologies for broadband reverberation data processing and analysis Baiju M. Nair* Naval Physical Oceanographic Laboratory, Kochi-682 021, India *[E-mail: baijumnair@gmail.com] Received 5 September 2014; revised 7 October 2014 Data processing methodologies used to analyse broadband reverberation signals from an explosive sound source are presented in this paper. Reverberation data was collected at deep (20 m) and shallow water (57 m) sites in the Bay of Bengal. In these experiments, TNT charges (0.4 kg) were used as sound sources. The received signals were recorded using two hydrophones deployed from the ship. The sonic surface duct thickness at the shallow water site is around 32 m with a limiting ray angle of 3.16 o and a lower cut off frequency at 416 Hz. The deep water location had deeper duct (63 m) with a limiting ray angle of about 4.47 o and a lower cut off frequency of 177 Hz. One third octave band analysis using multirate filters and time frequency analysis were used to study the reverberation characteristics. Comparison of deep water and shallow water reverberation characteristic across a broad band of frequencies are presented along with analysis based on ray modelling. [Keywords: Multirate filters, ray modelling] Introduction Performance of active sonar is considerably influenced by reverberation. Accurate prediction of active sonar performance requires the knowledge of sea surface and bottom scattering that govern the reverberation. Explosive charges have been in use for a long time as broadband sound sources in underwater acoustics research. Several reasons exist for their wide spread popularity such as broad bandwidth and highenergy density, ease of deployment, and relatively low cost. In order to make meaningful measurement, it is essential to know accurately the source levels of these charges. Since direct experimental measurement of the source levels of such shallow charges is inherently difficult, source levels have instead been obtained from the modelling of explosive charge waveform. The objective of this paper is to present data processing techniques required to analyse the broad band reverberation data collected at deep water and shallow water sites in the Bay of Bengal using explosives. One third octave band analysis between Hz to 12.5 khz was carried out on these signals. In deep water, ray paths of the sound from the source to bottom, and back to the receiver, are relatively few and can be easily visualized. The grazing angle of the sound on the seafloor, which together with the frequency and bottom type determines the bottom back scattering strength, is readily determined from the geometry or the ray diagram. In shallow water, however, the problem is not simple. Here many ray paths exist to and from the area of bottom that return sound at any particular instant of time 1. Large collection of literature is available on experiments conducted with explosives. Data/model comparison of reverberation has been described by Francine et al. 2 based on underwater explosion. Mackenzie 7 describes bottom reverberation returns for various frequencies. Chapman and Harris 8 described surface backscattering strength measurements using explosives. A data model comparison specific to shallow water reverberation was presented by Liu 9. Long range reverberation data gathered using towed array for various frequencies have been described by Preston et al. 10,11. These papers describe the measurement methodologies, extraction procedure and modelling methodology for reverberation data extracted on a towed array. A relatively low focus has been devoted to the presentation of signal processing aspects of the data analysis in all these papers or in the literatures available. The driving impetus for the present work was to rapidly assess the environment, i.e., to obtain tactically important data in short time frame using explosive charges. Description of the experiments Experiments were conducted to study the reverberation characteristics at deep water and

246 INDIAN J. MAR. SCI., VOL. 44, NO. 2 FRBRUARY 2015 shallow water sites. Explosive charges (TNT 0.4 kg) were used as the sources which were expended from the ship. The first experiment was conducted at the deep water site with an average depth of the water column of 20 m. The signals were recorded at two hydrophones at depths 13 m and 29 m. CTD profiles were taken at both locations and the sea state during the experiments was observed to be 01. The second experiment was conducted at shallow water where the average depth of the water column was 57 m. Miniature depth sensors were used for accurate depth measurements of hydrophone lowered from the deck of the ship. The signals were recorded using a high speed Sony tape recorder with a sampling rate of 48 khz. in various frequency bands of interest. Direct experimental source level measurement of explosive charges is inherently difficult. The received signal at any nearby hydrophone will receive the direct as well as the surface reflected path. Source levels have instead been obtained from modelling of the explosive charge waveform. The source signal levels were estimated based on simulated acoustic pressure time (p-t) waveform. The inputs for the source level computations are weight of the explosive used and depth of explosion 14. The generated time series is Fourier decomposed and corrected for spherical spreading (20logR, where R is the range from the explosion) to get the SL. The modelled output source level was validated with the experimental results available in the literature. Results from the Asian Seas International Acoustics Experiment in East China Sea-ASIAEX 2001 15 are compared with the modelled results. The p-t waveform can be modelled based on the equation from either Chapman 8 or Wakeley 16. Source level from Wakeley equation was found to match better with the experimental results. The source level spectra for the explosives (0.4 kg) used in the present experiment is presented in Fig. 2 Fig. 1 Sound speed profiles at the experimental sites. The sound speed profile (SSP) is presented in Fig. 1 and the zoomed version (first 1 m water column) of the same is also presented. From the SSP it is observed the deep water site with deeper duct had a larger limiting ray angle of about 4.47 o with lower cut off at 177 Hz. The surface duct was observed to be around 63 m. The duct thickness for the shallow water site was around 32 m, with limiting ray angle of 3.16 o and lower cut off frequency at 416 Hz. The bottom sediment observed at both the locations is coarse sand. Data processing methodologies Analysis of the received signal time series was carried out to study the reverberation characteristics. The quality of the data was studied before analysis and the final analysis is carried out only on specific datasets which contain all the relevant parameters. The first step of analysis is to estimate the exact source level of the explosives Fig. 2 Simulated source spectrum 16 (at 1m) for explosives used in the experiments (SL in unit db ref μ Pa 2 /Hz @ 1 m). Time frequency analysis Time frequency analysis ( Hz-15 khz) was carried out for the broadband explosive signals. The reverberation levels were recorded with the sampling frequency of 48 khz. Figs. 3 and 4 presents signal strength as a function of time and frequency in the deep water site and shallow water sites respectively. The depth of explosion was 9 m. The first bottom bounce and the second bounce are clearly visible in the case of deep water. Between the direct pulse (0-0.5 s)

BAIJU: BROADBAND REVERBERATION PROCESSING 247 and the first bounce (2.6 s), a small patch is seen from1.0 khz till around 8.0 khz (Fig. 3).This is the sound from the surfacing of the bubbles. An increase in reverberation level is seen around 10-12 s and a sudden fall thereafter. Fig. 4 presents the time frequency analysis of signal recorded at the, shallow water site. Features such as first and second bounce are not resolvable in shallow water. at frequency f s, with an adequate anti-alias filter (AAF). First, the one third octave components Fig. 4 Time frequency analysis of signal recorded at the shallow water site. Features such as first and second bounces are not resolvable in shallow water. Fig. 3 Time frequency analysis of signal recorded at the deep water site. Features such as first and second bounce are resolvable. One-third octave band analysis In order to analysis reverberation returns from individual frequency and study the reverberation characteristics as a function of frequency multirate one-third octave band analysis is done. One third octave band analysis 17 was carried out on the broad band explosive signal. Discrete Fourier Transform (DFT) is a constant absolute bandwidth frequency analysis methodology with a linear frequency scale. For the analysis of broad band reverberation from explosion, it is desirable to perform a constant relative bandwidth frequency analysis on a logarithmic frequency scale. One third octave filters are constant percentage or constant relative band width pass band filters, i.e., the ratio of the band width of a one third octave filters to its central frequency f c is equal to a constant, namely, (2 1/6-2 -1/6 ) = 0.23. This means that, in the low frequencies, the absolute band widths of the filters becomes extremely narrow. To obtain an efficient digital implementation of constant percentage filters (one-third octave filters), a multirate filter bank (Fig. 5) can be used. The multirate approach 17 is commonly used in dedicated digital frequency analysers. It takes advantage of the special structure existing in the one third octave filter bank to provide better filter characteristics at lower computational cost. The signal is sampled in the highest frequency band are computed. These high frequency components can then be discarded by a low pass (LP) filter. Once the highest octave components have been filtered away, it is possible to down sample the signal by a factor of 2. This is equivalent to changing the sampling frequency from f s to f s /2. The characteristics of a digital filter frequency with given coefficient are defined only in relation to the sampling frequency, which is now equal to f s /2. Thus, set of filter coefficients that yielded three one-third octave in the highest octave will now yield three one-third octave band filters (OBF1, OBF2 and OBF3), one octave lower in absolute frequency. Iterating the process will provide the one-third octave filter in the subsequent lower octaves. The signal filtered in one-third octave band is reduced by bandwidth factor to make the level in db/hz. Fig.5 Schematic of implementation of multirate one-third octave filter bank. The time series of reverberation level processed using filter banks are presented for deep water and shallow water (Figs. 6 and 7). Uniform smoothing of the signal is done with

248 INDIAN J. MAR. SCI., VOL. 44, NO. 2 FRBRUARY 2015 20 samples ( ms) at the band level by moving average method. The variance in the signal is found more at low frequencies than at the higher frequencies. The received level is then normalized to have uniform source level across different frequency bands. This is a requirement since the source levels of the explosives are not uniform across the frequencies. Source level (SL MOD ) for each frequency is obtained by modelling the explosive source. Received reverberation levels (Rx) from experimental data are subtracted from the modelled SL MOD for each frequency. The signal level so estimated is again reduced from a fixed value SL FIX (reference value). Reverberation returns finally obtained appear to be from a source of constant level across all frequencies. RL(f) = SL MOD (f) Rx(f) (db/hz) (1) RL NORM = SL FIX RL(f) (db/hz) (2) where Rx(f) is the received acoustic level (db/hz) at the hydrophone. SL MOD is the source level modelled based on Wakeley s equation corrected to spectral level. RL(f) is the reverberation level due to different source levels at different frequencies. Comparison between reverberation returns at different frequencies is not possible using RL(f) because explosive charges have different source levels for different frequencies. In order to have uniform source levels across different frequencies a source level normalization is done (2). SL FIX may be fixed to be a level higher than the maximum value of source level SL MOD and is taken as reference level. The received reverberation level is as though SL FIX is transmitted uniformly across all frequencies and RL NORM is received. Source depth - 09m Receiver depth - 13m Channel depth - 20m 0.5kHz 1.0kHz 3.15kHz 10.0kHz Fig. 6 presents the reverberation level in db/hz for various one-third octave centred frequencies. Low frequencies show higher reverberation level than the high frequencies. In the deep water as evident from Fig. 6, direct signal from the source reaches the hydrophone after 0.5 s, which also includes bubble pulses. The reverberation level (RL NORM ) falls in amplitude level from 0.5 s to 2.6 s where the contribution is only by surface and volume scattering. At around 2.6 s a strong signal is received corresponding to the first direct returns from bottom. Subsequently at 5.2 s, the second bottom bounce is observed. The RL NORM is approximately 20 db below the first return at low frequency, but increased to almost 30 db at higher frequencies. At around 2 s before the onset of bottom path (see also Fig. 3), there is an increase in signal level. This rise in level starts at 1.0 khz which reaches maximum at around 3.15 khz with 20 db rise from back ground and then disappear after 8 khz. This rise may be due to the breaking of smaller surface bubbles, after the bigger bubbles from the explosives reach the surface. At 3.15 khz the second bottom bounce appears as a sharp peak; unlike the low frequencies (less than 1.0 khz). Low frequencies have a broad level with no sharp features. The second bounce seems to have disappeared for high frequencies (more than 6 khz). In the case of shallow water, the lower frequency reverberation levels fall gradually but the higher frequency above 3 khz, the RL NORM falls is steeper. Source depth - 09m Receiver depth -19m Channel depth - 57m 0.5kHz 1.0kHz 3.15kHz 10.0kHz Fig. 7 Shallow water reverberation spectrum levels (db/hz) at selected one-third octave center frequencies plotted against time for the receiver depth of 19 m. Fig.6 Time series of deep water reverberation spectrum levels (db/hz) at selected one-third octave centre frequencies for the receiver depth of 13 m.

BAIJU: BROADBAND REVERBERATION PROCESSING 249 Comparison of deep water and shallow water reverberation with ray modelling Analysis of deep water reverberation Modelling of the ray path in the medium with the appropriate SSP at the site presents the area of insonification due to the source (Fig. 8). Though the explosive source is an omni-directional source, rays from - o to + o (from the horizontal axis) are only presented to highlight certain effect of ducted propagation on the reverberation time series. The direct path from the source to the bottom and back to the receiver (not shown in Figure) should arrive after 2.6 s corresponding to water column depth of 20 m. The second returns (source-bottom-surfacebottom receiver) should arrive after 5.2 s. Due to the strong positive gradient in the sound speed profile rays less than critical angle are trapped in the duct and the rest will pass through the duct to reach the bottom. The rays penetrating below the duct will travel to a range of not more than 9-10 km (R L ) as indicated in Fig. 8. The reverberations coming from the bottom will start after 2D/10 s, where D is the water column depth and will persist till about 2*R L /10. This will correspond to a travel time of about 12-13 s. The rays marked in blue and black colour in Fig. 8 undergo bottom interaction and contribute to the bottom reverberation. Rays in black colour initially travelled to the surface immediately after the explosion, but after the surface reflection they travel downwards along with the blue rays reaching a maximum range of R L. The rays from this omni-directional source interact with bottom refraction of sound rays in presence of the SSP gradient, and a shadow zone is present beyond that range at the bottom. The total two way travel distance from the source to R L is approximately 18.5 km corresponding to a travel time of 12 s (approx). Ranges beyond R L will not contribute for the first bounce scattering process, thereby causing a sudden decrease in reverberation level. The flat plateau (Figs. 3 and 6) till 12 s followed by steep fall in the reverberation level in deep water is visible at the lower frequency (within 6 khz). This strong reverberation return will have major consequences on the reverberation limited sonar performance. The second bottom bounce in distinctly visible at 3.0 and 6.3 khz. Rays marked in green have surface interactions and propagate in the surface duct. They interact with the surface and the volume (bubbles, suspended sediments etc) causing surface reverberation and volume reverberation. The back scattering strength from surface will be low due to the small angle of interaction at low sea state. So the expected surface reverberation should be low in comparison with bottom reverberation. Analysis of shallow water reverberation Multipath interaction from surface and bottom in shallow water makes ray modelling more complicated. Surface arrivals and bottom path are not easily separable as seen in Fig. 9. Fig. 8 Ray diagram of the acoustic propagation in the deep water site for a source located at 09 m depth. Depth of the ocean channel is 20 m. Green colour path is the ducted propagation path. Black colour is the surface-bottom channel path. for all horizontal ranges from 0 to R L m. No direct rays reach the bottom beyond R L due to the Fig. 9 Ray diagram of the acoustic propagation in the shallow water site for a source located at 09 m depth. Depth of the ocean channel is 57 m. Green color is the ducted propagation path. Black color is the surface-bottom channel path. The influence of the SSP may not be predominant in the reverberation decay. In deep water reverberation characteristics, multiple peaks were seen corresponding to various bounces between the acoustic waveguide whereas the shallow water reverberation return has a smooth

2 INDIAN J. MAR. SCI., VOL. 44, NO. 2 FRBRUARY 2015 decay. The direct pulse and the other scattering signals are not resolvable. The multiple scattering between the top surface and the bottom boundary is merged together. Shallow water reverberation returns are plotted for various frequencies (Fig. 7). Low frequencies show higher reverberation level than the high frequencies. The bottom sediment at the in-situ location is coarse sand. Ellis et al. 1 describes very less dependency of reverberation on frequencies and depth in Pekeris channel in an iso-velocity channel. However the presence of a very strong duct and low loss bottom indicate strong frequency dependence on reverberation returns. Deep (20 m ) Shallow (57 m) Fig. 10 Comparison between deep water and shallow water reverberation returns at 1.0 khz. Lower frequencies show a very slow and gradual fall in reverberation levels as compared with the high frequencies (Fig. 7). The effect of lower frequency reverberation is dominant for almost 10 s after the event, corresponding to a range of 7.5 km. This can be crucial factor in the design of low frequency active sonar especially in the shallow water scenario. Even though the low frequencies have higher propagation ranges, this may not be favourable in the case of active sonar, specifically if the target is nearer. The closer targets may be masked in the strong reverberation returns as seen in this ducted shallow water scenario. Reverberation level of 66 db at 0.5 khz is received as compared to 58 db at 3.15 khz even after 2 s. Reverberation level comparison in shallow and deep waters The comparison of reverberation levels at deep and shallow water sites are presented in Figs. 10, 11, 12. Fig. 10 corresponds to the reverberation levels from deep water and shallow water for 1.0 khz. Reverberation Levels of shallow water are comparatively higher except at the first bottom bounce. It is stronger in case of deep water than shallow water near 13 sec due to the effect of ducted propagation. After 13 sec a sudden fall in level is seen in case of deep water as compared to shallow water, where such effect of duct is not predominant thought there was a duct at 32 m. This can also be inferred from the ray plot (Fig. 9). At 3.15 khz (Fig. 11) the first and second bottom bounce has significant higher level of reverberation returns compared to shallow water. The reverberation decay is faster in the initial ranges for shallow waters thereafter it is almost steady for longer ranges. Higher frequency reverberation (10.0 khz) shows significant level difference between shallow water and deep waters (Fig. 12).The second bottom bounce is not present as the propagation loss at these higher frequencies is higher. Deep(20 m) Shallow (57 m) Fig. 11 Comparison between deep water and shallow water reverberation returns at 3.15 khz. Deep (20 m) Shallow (57 m) Fig. 12 Comparison between deep water and shallow water reverberation returns at 10.0 khz. Conclusions Reverberation time series analysis is presented for a broadband source. Multirate filter bank technique is used to achieve the one third octave band filters for analysis across wide band. Reverberation characteristic in deep water and

BAIJU: BROADBAND REVERBERATION PROCESSING 251 shallow was correlated with ray model results. Steep fall in reverberation level at shallow water as the frequency increases is clearly evident from the octave band analysis. Sharp peak and hump in the deep water reverberation returns is presented. The calibrated experimental results can be used to validate the models developed across a wide band of frequencies. Experimental comparison brought out various features such as effect of ducted propagation, frequency dependence to deep water and shallow water reverberation characteristics. Acknowledgements The author thanks Shri. S. Anathanarayanan, Director, NPOL, for the permission and encouragement to present this work. The author acknowledges the support and guidance provided by Dr. M.P. Ajai Kumar, Scientist G. References 1. Ellis D.D., A shallow-water normal-mode reverberation model. J. Acoust. Soc. Am., 97(1995): 24 2814. 2. Francine Desharnis and Dale D. Ellis, Data- Model Comparison of reverberation at three Shallow-Water sites. IEEE J. Ocean. Eng.,22 (1997). 3. Feng-Hua LI, and Jian Jun LIU, Bi-static reverberation in shallow water: Modelling and Data comparison. Chin. Phys. Lett,19(2002):1128-1130 4. Brekhovskikh L. and Lysanov Y., Fundamentals of Ocean Acoustics. NY, Springer-Verlag(1982). 5. Jensen F. B., Kuperman W.A., Porter M. B., and Schmidt H., Computational Ocean Acoustics. NY: A.I.P. Press(1994) 6. Urick R.J., Principles of Underwater Sound, 3rd ed., New York: Mc Graw-Hill(1983) 7. Mackenzie K.V., Bottom Reverberation for 530 and 1030-cps Sound in Deep Water. J. Acoust. Soc. Am., 33(1961): 1498 14. 8. Chapman P. and Harris J.H., Surface back scattering strengths measured with explosive sound sources. J. Acoust. Soc. Am., 34(1962): 1592 1597. 9. Li F., Liu J., and Zhang R., A model/data comparison for shallow-water reverberation. IEEE J. Ocean. Eng., 29(2004): 10 1066. 10. Preston J.R. and Ellis D.D, Extracting bottom information from towed array reverberation data Part I : Measurement methodology. J Marine Science, 78(2008). 11. Preston J.R. and Ellis D.D., Extracting bottom information from towed array reverberation data Part II: Extraction procedure and Modelling methodology. J Marine Science, 78(2008). 12. McDaniel S.T., Sea surface reverberation: A review. J. Acoust. Soc. Am., 94(1993): 15 1922. 13. Ellis D.D., and Preston, J.R, Extracting sea-bottom information from reverberation data. J. Acoust. Soc. Am., 105(1999):1042. 14. Internal Report, DRDO/NPOL/OA/ RR/ 09/11. 15. Zhaohui Peng, Ji-Xun Zhou, Peter H Dahl and Renhe Zhang, Sea-Bed acoustic parameters from dispersion analysis and transmission loss in the east china sea. IEEE J. Oceanic Engg., 29 (2004). 16. Wakeley Jr J., Coherent ray tracing - measured and predicted shallow-water frequency spectrum. J. Acoust. Soc. Am., 63(1978):1820 1823. 17. Christophe Couvreur, Implementation of one third octave filter band in MATLAB, http: //tcts.fpms.ac.be:10/matlab/octave.html.